Question

USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONS

Vito Scaletta just bought his dream car, 2019 Aston Martin DB9 that cost $208,700. He paid $30,000 down and financed the balance over 84 months at 6.25% p.a. (Assume that Vito makes all required payments on time).

What will the balance on Vito’s loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?

Answer 1

Step-1:Calculation of monthly payment
Monthly payment	=	Loan amount	/	Present value of annuity of 1
	=	$       1,78,700	/	67.89554419
	=	$       2,631.98
Working:
Loan amount	=	Cost of Car	-	Down payment
	=	$       2,08,700	-	$           30,000
	=	$       1,78,700
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.005208)^-84)/0.005208		i	6.25%/12	=	0.005208
	=	67.89554419		n		=	84
Step-2:Calculation of balance of loan at the end of fourth year
Loan balance is always present value of remaining monthly payment.
Loan balance	=	Monthly payment	x	Present value of annuity of 1
	=	$       2,631.98	x	32.74913262
	=	$     86,195.20
Working:
Present value of annuity of 1 for remaining time	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.005208)^-36)/0.005208		i	6.25%/12	=	0.005208
	=	32.74913262		n	84-48	=	36
So,
Balance on Vito’s loan will be at the end of the fourth year $ 86,195.20